The change in multiplicity of an eigenvalue due to adding or removing edges

Charles R. Johnson, Carlos Manuel Saiago, Kenji Toyonaga

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the change in the multiplicities of the eigenvalues of a Hermitian matrix with a simple graph G, when edges are inserted into G or removed from G. We focus upon cases in which the multiplicity of the eigenvalue does not change due to inserting or removing edges incident to a vertex. Furthermore, we show how the change in the multiplicities of the eigenvalues occur, when two disjoint graphs are connected with one edge, based upon the status of the vertices that are connected. Lastly, we give the possible classifications of cut-edges in a graph and characterize the occurrence of each possible status.

Original languageEnglish
Pages (from-to)86-99
Number of pages14
JournalLinear Algebra and Its Applications
Volume560
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Cut-edge
  • Edge
  • Eigenvalues
  • Graph
  • Hermitian matrix
  • Multiplicity

Fingerprint Dive into the research topics of 'The change in multiplicity of an eigenvalue due to adding or removing edges'. Together they form a unique fingerprint.

  • Cite this